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The phase problem and the Patterson function

Dennis Sherwood and Jon Cooper

in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.003.0012
Subject:
Physics, Crystallography: Physics

This chapter demonstrates that the experimental observable in diffraction analysis is the intensity of each diffraction spot which provides only the amplitude of the corresponding structure factor ... More


Solving the phase problem experimentally

Dennis Sherwood and Jon Cooper

in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.003.0014
Subject:
Physics, Crystallography: Physics

This chapter covers methods of structure solution which are used when molecular replacement is impossible, usually due to the lack of a suitable search model. These methods require that additional ... More


Fourier transforms and convolutions

Dennis Sherwood and Jon Cooper

in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.003.0005
Subject:
Physics, Crystallography: Physics

This chapter revisits the essential mathematics of integral calculus and introduces the important concept of the Fourier transform, the properties of which are elegantly demonstrated by sketching the ... More


Incommensurate Crystallography

Sander van Smaalen

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570820
eISBN:
9780191718762
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570820.001.0001
Subject:
Physics, Crystallography: Physics

Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the ... More


Patterson methods in powder diffraction: maximum entropy and symmetry minimum function techniques

Michael A. Estermann and William I. F. David

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

Starting from a definition of the relationship between a crystal structure and its Patterson function, this chapter considers the role of the Patterson function in the particular context of powder ... More


METHODS OF STRUCTURE SOLUTION

Sander Van Smaalen

in Incommensurate Crystallography

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570820
eISBN:
9780191718762
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570820.003.0010
Subject:
Physics, Crystallography: Physics

This chapter provides an overview of the methods of structure solution of incommensurately modulated crystals and composite crystals. Assuming the periodic average structure is known, it is shown ... More


Fourier syntheses

William Clegg

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0008
Subject:
Physics, Crystallography: Physics

A diffraction pattern is the (forward) Fourier transform of a crystal structure, obtained physically in an experiment and mathematically from a known or model structure (providing both amplitudes and ... More


Symmetry and reflection conditions in reciprocal space

Paolo G. Radaelli

in Symmetry in Crystallography: Understanding the International Tables

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199550654
eISBN:
9780191775093
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550654.003.0011
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter focuses on symmetry in reciprocal space. It reviews the definitions of reciprocal space and dual (reciprocal) basis vectors (from Chapter 6), and presents the new concept of the ... More


Fourier analysis in diffraction and image formation

Christopher Hammond

in The Basics of Crystallography and Diffraction

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198738671
eISBN:
9780191801938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738671.003.0013
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter starts with the Fourier series and Fourier transforms, and the representation of periodic functions. It then looks at Fourier analysis in crystallography. It details electron density, ... More


Molecular replacement

David Blow

in Outline of Crystallography for Biologists

Published in print:
2002
Published Online:
November 2020
ISBN:
9780198510512
eISBN:
9780191919244
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198510512.003.0014
Subject:
Chemistry, Crystallography: Chemistry

The methods described in the Chapters 7 and 8 are the only ones practicable when the structure under study is completely unknown. But as soon as a few ... More


Density-modification procedures: improving a calculated map before interpretation

David Blow

in Outline of Crystallography for Biologists

Published in print:
2002
Published Online:
November 2020
ISBN:
9780198510512
eISBN:
9780191919244
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198510512.003.0015
Subject:
Chemistry, Crystallography: Chemistry

Procedures to determine the phases of the structure factors, by isomorphous replacement, by anomalous scattering, or by molecular replacement, were ... More


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